Mereological Extensionality, Supplementation, and Material Constitution

Abstract

I want to defend the claim that constitution is not identity: that, for example, a bronze statue, S, is not identical with the lump of bronze, B, that constitutes S at a given time /. My reasons for claiming that constitution is not identity are the usual ones, namely, that objects which stand in the constitution relation to one another possess different identity and persistence conditions and consequently typically differ in respect of their historical and modal properties.1 But anyone who defends such a claim owes us a perspicuous account of what the constitution relation is, given that it is not identity. Elsewhere, I have proposed the following definition - and here I should emphasize that I am now concerned only with material constitution, as exhibited in the statue/lump case:2[MC] x is materially constituted by y at t =d^sub f^x and y coincide spatially at t and every proper part of y at Ms a proper part of x at t but not every proper part of x at tis a proper part of y at t.An attractive feature of [MC] is that it makes material constitution an asymmetrical relation, as it surely should be: if the lump of bronze, B, constitutes the bronze statue, S, then it should follow mat S does not likewise constitute B. Another attractive feature of [MC] is that it appeals only to familiar spatiotemporal and mereological relations, rendering it suitably perspicuous. Yet another attractive feature of [MC] is that it does not require us to abandon the mereological principle of Weak Extensionality, which may be stated thus:3[WE] If x and y have proper parts at t and x is not identical with y, then x and y do not have exactly the same proper parts at t.Some philosophers who maintain that constitution is not identity do so at the expense of rejecting [WE], holding that when one object materially constitutes another they possess exactly the same proper parts: but this lays such philosophers open to criticism from mainstream mereologists, by whom [WE] is widely accepted. However, [MC] will be acceptable only if, in a case like that of the bronze statue and the lump of bronze, we can convincingly argue that the material constitution relation, as defined by [MC], does indeed hold between the objects in question. And this is the issue that I now intend to address.1. The Paring Down ArgumentElsewhere, I have offered what might appropriately be called the Paring Down Argument in favour of the claim that the bronze statue, S, and the lump of bronze, B, are indeed related as [MC] requires them to be in order for ? to materially constitute S.4 [MC] requires that S and B, at the time t at which ? materially constitutes S, differ with respect to their proper parts - and, more specifically, that S possesses proper parts at t which are not possessed by ? at t, although not vice versa. In defence of this claim, I have cited such parts of 5 as its head, H, which is clearly a proper part of S but not, I maintain, a proper part of B. At this point it is helpful to introduce a terminological distinction between (what I shall call) 'material' parts and 'anatomical' parts. A material part of the lump of bronze ? is just any part of ? that is itself a portion of bronze, such as the portion of bronze, BH, which coincides with and indeed materially constitutes H, the head of the statue S. By contrast, an anatomical part of the statue S is a part such as its head, H, or one of its arms. I shall try to define 'anatomical part' more precisely later. The Paring Down Argument is designed to persuade us that, for example, 5s head, H, while it is a proper part of the statue S, is not a proper part of the lump of bronze, B.Here is how the Paring Down Argument proceeds in the case of this example. Suppose, for reductio, that H is a proper part of B. Then, surely, H should be a part of each member of a series of ever smaller material parts of ? converging upon and including BH, the material part of ? that constitutes S's head, H. …